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Integral Inverse

  1. Sep 7, 2007 #1
    commonly we have:
    [tex]\int^t_0 \ dx=M[/tex]

    "M" is a specific number (the result of integal)

    my question:
    having value of "M", how we can find the "t" value
  2. jcsd
  3. Sep 7, 2007 #2


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    Homework Helper

    This sounds much like homework to me. >"<

    What have you done? Have you tried anything?

    Ok, I'll give you some hints then:

    1. What is the anti-derivative of: [tex]\int dx = ?[/tex]

    2. What is : [tex]\int_0 ^ t dx = ?[/tex] in terms of t?

    3. What is the relation between t, and M?
  4. Sep 7, 2007 #3


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    Staff Emeritus
    Science Advisor

    In case this isn't homework and is a question from curiosity: In general, there is a function being integrated; [tex]\int^t_0 f(x) dx=M[/tex]. In which case, the answer to your question is "only if we know the function, f."
  5. Sep 7, 2007 #4
    i know the function f(x)
    suppose that f(x) is x

    [tex]\int^t_0 x dx=M[/tex]
  6. Sep 7, 2007 #5


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    Science Advisor

    What IS the integral (anti-derivative) of x? Do the integration on the left, set it equal to M and solve the equation for t.

    In the very simple case, you started with, [itex]\int_0^t dx[/itex], the anti-derivative of the constant 1 is just x
    [tex]\int_0^t dx= x\right|_0^t= t[/itex]
    In that case, whatever number M is, you have t= M. For the case of
    [tex]\int_0^t x dx= M[/tex]
    it is almost as simple.
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